yup, lime is for acid neutralization.
Heat stop II on everything below and above thimble.
yes, the expansion issues are non-existant below thimble, I typically mortar the flue tight below the thimble.
The fine vermiculite is what you want.
you could fill the cores in the block w/ vermiculite if that makes you feel better, if you want to do it, do it.
Use type S mortar or harder, do NOT use type N if you want your chimney to last.
Avoid rebar in the cores - rebar in a stack is great if you can keep it far away from any potential heat, if you cant, (which you can't as the cores in the block are far less than the recommended 6") then just don't use it.